Shortly after his political nemesis, President Yoon Suk Yeol, declared martial law last Tuesday, Lee Jae-myung began livestreaming from his cellphone. While driving to the National Assembly, the leader of South Korea’s main opposition party appealed to Koreans to rush to the Assembly and hold back soldiers trying to seize the parliament.

“You must protect the Assembly, the last line of defense for our democracy,” Mr. Lee said repeatedly — in a watershed moment for South Korean democracy and for his own political career. Mr. Lee’s exhortation, relayed by YouTubers, helped attract crowds who slowed down the advance of troops and bought time for lawmakers to vote down Mr. Yoon’s martial law​ decree, forcing the president to withdraw it after just six hours​​.

Mr. Lee, who has been fighting legal charges that he says are politically motivated, now finds himself in a stronger political position than ever. His party holds the majority in the Assembly and he represents what most South Koreans want: Mr. Yoon removed from office. Polls show he is most favored to win if a presidential election is held now.

With political turmoil still roiling around him, Mr. Lee looked calm and in control this week — and determined to oust Mr. Yoon quickly. But his party’s first attempt to impeach Mr. Yoon failed on Saturday, when the president’s party boycotted the parliamentary vote. Mr. Lee’s Democratic Party plans to organize an impeachment vote every Saturday.

“We will keep doing this until he is impeached,” Mr. Lee said in an interview at his Assembly ​office on Monday. “More people are joining in the struggle with growing fervor. We will try to get this done by Christmas.”